Suppose fx=x+12 for x≥-1. If g(x) is the function whose graph is the reflection of the graph of f(x) withrespect to the line y = x, then g(x) equals
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a
1-x-1,x≥0
b
1x+12,x>-1
c
x+1,x≥-1
d
x-1,x≥0
answer is D.
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Detailed Solution
Given that fx=x+12,x≥-1.Now, if g(x) is the reflection of f(x) in the line y = x, theng(x) is an inverse function of y = f(x).Given y=x+12 x≥-1 and y≥0or x=±y-1or gx=f-1x=x-1, x≥0